Program Perspectives on Quantum Information

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Program Perspectives on Quantum Information

• Michael Foster
• National Science Foundation

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Outline

• Computing Communication Foundations
• QIS Bumper Stickers
• Quantum Computing
• Quantum Key Distribution
• Support agencies
• Where next?

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Why Foundations?
-

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Foundations Everywhere
Infrastructure
Systems
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Quantum InformationBumper Stickers

• Quantum computation
• State superposition provides parallelism
• Quantum communication
• No cloning theorem provides unforgability
• Quantum metrology
• Entanglement provides consistent measurement

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Quantum Computation
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QIP and Moores Law
General Architecture
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CMOS ICs
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Lattice-Gas Architecture
TX-2
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QC Roadmap
1
MIPS
ENIAC
Quantum Dots
10-3
Conventional Computer Roadmap
10-6
Differential Analyzer
1850
2000
1900
1950
2050
Babbage Engine
Year
Liquid NMR
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Power of Qubits

• Qubit state of a quantum two-level system

Continuum of states!
1 classical bit has two states 0 and 1 1 qubit
has infinitely many states!

• Physical realizations of qubits
• photon polarization
• electron spin
• nuclear spin
• pair of electron states in a trapped ion/atom
• magnetic flux state in a Josephson junction ring
• Cooper pair number states, etc.

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Power of Qubits

• Multiple qubits

A classical 3-bit state 001 A
quantum 3-qubit state
N qubits is worth 2n classical bits!

• Entanglement

Not entangled
Entangled!
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Power of Quantum Computation

• Quantum Parallelism

2n values of F(x) all in one go!!
An exponential amount of computation has been
achieved in the time it takes to compute the
function on a single input!
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Quantum Complexity
Provably Q-hard algorithms
Protein Folding?
Graph Isomorphism?
BQP
PSPACE
NP
P
Factorization (Shor)
AjtaiDwork Coding?
NP? BQP?
Unsorted Search (Grover)
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QIP An Example Algorithm

• Permutation Order-Finding (Chuang et al, 00)
• Permutation ? is an operation that rearranges a
  set of objects
• Order r of a permutation applied to element y of
  a set is the minimum number of times ? must be
  applied to put y back in its original position
• Problem has wide range of applications
  (Cryptography)

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Classical versus Quantum

• Quantum approach
• Order is the period of a function
• fy(x) ?x(y)
• Quantum Fourier Transform allows us to find
  periods of all ?x(y) with one transform
• Exponential speedup-- Minimum number of steps
  proportional to bits in y

• Classical approach
• Series of trials to find the x-th permutation
  ?x(y).
• Find equality. When ?a(y) ?b(y) then ord(?)
  a-b
• Number of trials needed increases exponentially
  with the number of bits representing y

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Classical Order-Finding
Classical approach
What a permutation really looks like
Check Equality
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Quantum Order-Finding
Equality
Quantum approach
Quantum Fourier Transform Checks Equality in
Parallel
Large Fourier Components
Likely result
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Quantum Fourier Transform (QFT)

• Variant of the Discrete Fourier Transform (DFT)
  that can be implemented on a quantum computer
• At the heart of Factoring and Order-Finding
  problems
• QFT transforms state amplitudes to state
  amplitudes
• NOT qubits to qubits

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QFT in Order Finding
Superpose
QFT
Measure
P
R
H
H
Answer
x
y
?x(y)

• States are measured according to their
  probability
• Many states at P produce the same ?x(y)
• QFT produces their frequency
• Probably answer reflects large number of states
  at P

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Status of Computing

• Proof of concept factoring (2001)

Chuang et al. 4-bit Shor algorithm implementation
(2001)

• Ongoing ion-trap implementation effort
• Some optical lattice efforts
• Solid-state spins moving slowly

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Ion Trap Investigations

• Done (per ARDA Roadmap April 2, 2004)
• 2-qubit operations demonstrated
• Long decoherence times in progress
• 3-10 qubit operations started
• Proposed (individual researchers)
• 10-20 qubit registers
• Architectures with 1000 circulating qubits
• Possibility
• 20 logical qubits (2-level error correct 1000
  qubits)
• 10 bit factoring

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Optical Lattices

• Done (individual researchers)
• 110 site lattice loaded from BEC with 200
  atoms/site
• Proposed (individual researchers)
• 8000 sites with CO2 lasers proposed by Berkeley
  QuIST project
• Filling factor 1/2
• Permits 80 logical qubits
• Permits 40 bit factoring

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Architectural Roadblocks

• Classical control
• Large feature sizes for control lines mean large
  computers
• Wiring and corners
• Moving qubits leads to decoherence
• Error correction
• More check bits than data bits
• Cumulative effect
• May need 100,000 times longer decoherence times
  than required by operations alone (Balensiefer
  et. al, ISCA32, 2005, pp186-196).

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Quantum Security
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Quantum Key Distribution

• Use unforgability to detect eavesdropping
• Shared generation of secure key
• Extensive classical processing

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Status of Key Distribution
BBN-AFRL-QuIST Network Rollout June 1, 2004
NEC 2-week demonstration May 31, 2005 (AFRL-QuIST
inside?)
ID Quantique Turnkey System Available throughout
Switzerland June 05
13kb/sec sifted key over 16km commercial access
optical network
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Support Agencies
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DARPA Mission
Focused strategic thrusts Specific
programs Emphasize transition
Source Bridging the Gap February 2005
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DARPA Organization
Source Bridging the Gap February 2005
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QIP in DARPA Organization
Source Bridging the Gap February 2005
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NSF Mission

• National Science Foundation Act of 1950 (Public
  Law 810507)
• To promote the progress of science
• to advance the national health, prosperity, and
  welfare
• to secure the national defense
• and for other purposes.

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NSF Organization
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QIP in NSF Organization
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CISE Mission

•  
• to enable the United States to remain competitive
  in computing, communications, and information
  science and engineering
• to promote understanding of the principles and
  uses of advanced computing, communications, and
  information systems in service to society and
• to contribute to universal, transparent, and
  affordable participation in an information-based
  society.

CISE has three goals
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Desired Project Characteristics

• DARPA Fast Results
• Military need
• Technical challenges and plan for meeting them
• Transition plan
• NSF Sustained Effort
• Asks fundamental questions
• Maintains U.S. competitiveness
• Societal need
• Broad participation

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DARPA Program Highlights
QuIST Network Rollout June 1, 2004
Chuang et al. 4-bit Shor algorithm implementation
(2001)
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NSF Program Highlights

• Institute for Quantum
• Information at Caltech

• Quantum Complexity and Polynomial Approximations
  of Boolean Functions
• Quantum and classical tradeoffs
• Classical simulation of quantum communication.
• Phase transition in biological signaling systems
• Education plan theory of computation courses

CAREER Award Yaoyun Shi at U. Michigan
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Where Next for Communication?

• DARPA
• Long range demonstrations between metronets
• GtoA and GtoS demonstrations
• ConOps for QKD
• NSF
• New protocols
• Security bounds

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Where Next for Computation?

• New algorithms
• Exponential speedups, please!
• (Hashing outdoes unstructured search)
• New applications of existing algorithms
• Pells equation
• Random walk
• Scalable architectures
• Controllable
• Fault tolerant
• Medium-scale implementations
• 10s of qubits
• Probably beyond NSF resources

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The Near Future

• NSF budget is down 3 in 2005, looks flat
• DoD will need transitions beyond crypto
• New algorithms and protocols are needed for the
  next push
• Scalable architectures too

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The Want Ads
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Program Directors Sought

• Numeric, Symbolic, Geometric computing
• Emerging Models and Technologies
• Interdisciplinary capability
• Across cluster, division, NSF, and globally

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Contact

• Vacancy announcements appear on www.nsf.gov
• Meanwhile contact
• Michael Foster
• Division Director
• Computing Communication Foundations
• National Science Foundation
• 4201 Wilson Boulevard
• Arlington, VA 22230
• 703-292-8910
• mfoster_at_nsf.gov